Hi Magnalf, I'm glad you read my paper and I hope you liked it.
The discussion related to entropy can be interesting, but it is another way of arriving at a solution to part of the problem. The equilibrium point is nonetheless based on a count of beats between harmonics, so doing it at runtime as tuners like Tunelab or Veritune do, or doing it by sampling sounds and then calculating them together, doesn't seem to me to change much about the matter. Certainly, sampling a certain number of sounds instead of just a few as Tunelab does can increase measurement sensitivity and certainly promises better results in terms of tuning accuracy. Now we have to see if this greater accuracy is truly justified in practice. I'll give an example... In any case, when tuning, one must consider the tuner's hand. To be fair, a tuner always tunes a note well within a margin of error relative to the frequency at which that string should theoretically vibrate. We are human and therefore there is a certain margin of error; I would say in the order of 2/4 cents. Now, if the measurement sensitivity increases to the order of tenths of a cent, you understand perfectly well that such accuracy is completely useless. It would be like asking you to measure the length of a desk to put in a room with a laser meter... It would be perfectly fine to measure it with a tailor's tape! It is useless to know that the desk is 10 meters long, 1 centimeter, 2 millimeters, and 234 thousandths of a millimeter! Moreover, in this context, but also in the context related to tuning, it could even be misleading! Climatic conditions change the physical variables at play, just as they would with the desk. If the temperature increased by one degree Celsius, probably the thousandths of a millimeter would no longer be 234 but 879, for example.
The point is that, by necessity, tuning with these software tools is still a hybrid tuning since they work very well only in the center. In the lows and highs, as I have repeatedly motivated and demonstrated even in my paper, it is necessarily the ear that commands. What I was suggesting in the paper could be, for example, conducting an acoustic test on the perception of the succession of ascending and descending octaves to the ear of the person about to tune. In this way, we could have software that behaves a bit like the tuner's ear by imitating it in these zones. The fact remains that for the tuning—let's call it "technological"—of this instrument, an absolutely definitive solution will probably never exist. Perhaps one day there will be pianos that are tuned by ear only the first time. They will memorize the frequencies set by the tuner and, as a note drops, they will retune themselves by comparing the recorded frequency with the current one. Even in this case, however, things will not work indefinitely. Every time a piano is tuned, the string becomes thinner and less disharmonious; rust can appear on the strings, and this also implies physical changes in their vibratory motion. In short, the good old tuner's ear seems irreplaceable so far. In any case, this latter "self-tuning" method could certainly be a good solution for those who use the piano at home for studying (not having to seek perfection). For concerts and concert pianos, however, it will always be necessary to call a tuner. Let's not forget that even if we somehow managed to solve the tuning problem, all the discussion regarding the preparation of the piano, its regulation, and the voicing of the hammers would remain. True craftsmanship can hardly be replaced by machines! But this is just my opinion.